Silicon crystallized in the usual cubic (diamond) lattice structure has dominated the electronics industry for more than half a century. However, cubic silicon (Si), germanium (Ge) and SiGe-alloys are all indirect bandgap semiconductors that cannot emit light efficiently. Accordingly, achieving efficient light emission from group-IV materials has been a holy grail 1 in silicon technology for decades and, despite tremendous efforts 2-5 , it has remained elusive 6 . Here, we demonstrate efficient light emission from direct bandgap hexagonal Ge and SiGe alloys. We measure a sub nanosecond, temperature insensitive radiative recombination lifetime and observe a similar emission yield to direct bandgap III-V semiconductors. Moreover, we demonstrate how by controlling the composition of the hexagonal SiGe alloy, the emission wavelength can be continuously tuned in a broad range, while preserving a direct bandgap. Our experimental findings are shown to be in excellent quantitative agreement with the ab initio theory. Hexagonal SiGe embodies an ideal material system to fully unite electronic and optoelectronic functionalities on a single chip, opening the way towards novel device concepts and information processing technologies.Silicon has been the workhorse of the semiconductor industry since it has many highly advantageous physical, electronic and technological properties. However, due to its indirect bandgap, silicon cannot emit light efficientlya property that has seriously constrained potential for applications to electronics and passive optical circuitry 7-9 . Silicon technology can only reach its full application potential when heterogeneously supplemented 10 with an efficient, direct bandgap light emitter.The band structure of cubic Si, presented in Fig. 1a is very well known, having the lowest conduction band (CB) minimum close to the X-point and a second lowest * These authors contributed equally to this work. † Correspondence to E.P.A.M.(e.p.a.m.bakkers@tue.nl).minimum at the L-point.As such, it is the archetypal example of an indirect bandgap semiconductor, that, notwithstanding many great efforts 3-6 , cannot be used for efficient light emission.By modifying the crystal structure from cubic to hexagonal, the symmetry along the 111 crystal direction changes fundamentally, with the consequence that the L-point bands are folded back onto the Γ-point. As shown in Fig. 1b, for hexagonal Si (Hex-Si) this results in a local CB minimum at the Γ-point, with an energy close to 1.7 eV 11-13 . Clearly, Hex-Si remains indirect since the lowest energy CB minimum is at the M-point, close to 1.1 eV. Cubic Ge also has an indirect bandgap but, unlike Si, the lowest CB minimum is situated at the L-point, as shown in Fig. 1c. As a consequence, for Hex-Ge the band folding effect results in a direct bandgap at the Γ-point with a magnitude close to 0.3 eV, as shown in the calculated band structure in Fig. 1d 14 .To investigate how the direct bandgap energy can be tuned by alloying Ge with Si, we calculated the band structures of He...

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Excitonic effects in optical spectra and electron-hole pair excitations are described by solutions of the Bethe-Salpeter equation (BSE) that accounts for the Coulomb interaction of excited electron-hole pairs. Although for the computation of excitonic optical spectra in an extended frequency range efficient methods are available, the determination and analysis of individual exciton states still requires the diagonalization of the electronhole HamiltonianĤ. We present a numerically efficient approach for the calculation of exciton states with quadratically scaling complexity, which significantly diminishes the computational costs compared to the commonly used cubically scaling direct-diagonalization schemes. The accuracy and performance of this approach is demonstrated by solving the BSE numerically for the Wannier-Mott two-band model in k space and the semiconductors MgO and InN. For the convergence with respect to the k-point sampling a general trend is identified, which can be used to extrapolate converged results for the binding energies of the lowest bound states.

Using quasiparticle band structures based on modern electronic-structure theory, we calculate the branch-point energies for zinc blende ͑GaN, InN͒, rocksalt ͑MgO, CdO͒, wurtzite ͑AlN, GaN, InN, ZnO͒, and rhombohedral crystals ͑In 2 O 3 ͒. For InN, CdO, ZnO, and also In 2 O 3 the branch-point energies are located within the lowest conduction band. These predictions are in agreement with observations of surface electron accumulation ͑InN, CdO͒ or conducting behavior of the oxides ͑ZnO, In 2 O 3 ͒. The results are used to predict natural band offsets for the materials investigated.

We compute optical properties including excitonic effects for the equilibrium polymorphs of three group-II metal monoxides by solving the Bethe-Salpeter equation. The underlying electronic structures are based on results of a recently developed GW approach starting from a hybrid exchange-correlation functional. The resulting quasiparticle band structures are discussed with respect to their mapping on computationally less expensive electronic structures computed using a GGA+ U method together with a scissor operator ⌬. The efficiency of the latter approach allows the computation of real and imaginary parts of the dielectric function including excitonic effects up to photon energies of 32.5 eV with high accuracy. In addition, we derive the reflectivity as an optical key quantity as well as the energy-loss function. For dominant peak structures we identify the valence bands that mainly contribute to the corresponding transitions. Furthermore, the influence of excitonic effects and the comparison with results from other calculations and measurements are discussed in detail. Chemical trends across the oxides are identified.

The study of the oxygen vacancy (F center) in MgO has been aggravated by the fact that the positively charged and the neutral vacancy (F+ and F0, respectively) absorb at practically identical energies. Here we apply many-body perturbation theory in the G0W0 approximation and the Bethe-Salpeter approach to calculate the optical absorption and emission spectrum of the oxygen vacancy in all three charge states. We observe unprecedented agreement between the calculated and the experimental optical absorption spectra for the F0 and F+ center. Our calculations reveal that not only the absorption but also the emission spectra of different charge states peak at nearly the same energy, which leads to a reinterpretation of the F center's optical properties.

The magnetic-ordering and orbital-occupancy induced distortions of the rocksalt structure below the Néel temperature are computed for antiferromagnetic MnO, FeO, CoO, and NiO by means of spin-polarized density functional theory including generalized-gradient corrections and an on-site Coulomb repulsion U . The important role of the occupation of the t 2g minority-spin states is studied in detail for the occurring rhombohedral and monoclinic distortions. The magnetic anisotropy energy is calculated to determine the orientation of the local magnetic moments in the antiferromagnetic crystals. We take into account both the influence of spin-orbit coupling and the transverse electron interaction. The spin-orbit interaction drives the magnetic anisotropy in CoO and FeO due to the partially filled t 2g subshell while transverse electron interaction plays an important role for the magnetic anisotropy in MnO and NiO due to the completely empty or filled t 2g subshell. The results for the structural and magnetic anisotropies are discussed in the light of the available experimental data.

High-quality defect-free lonsdaleite Si and Ge can now be grown on hexagonal nanowire substrates. These hexagonal phases of group-IV semiconductors have been predicted to exhibit improved electronic and optical properties for optoelectronic applications. While lonsdaleite Si is a well-characterized indirect semiconductor, experimental data and reliable calculations on lonsdaleite Ge are scarce and not consistent regarding the nature of its gap. Using ab initio density-functional theory, we calculate accurate structural, electronic, and optical properties for hexagonal Ge. Given the well-known sensitivity of electronic-structure calculations for Ge to the underlying approximations, we systematically test the performance of several exchange-correlation functionals, including meta-GGA and hybrid functionals. We first validate our approach for cubic Ge, obtaining atomic geometries and band structures in excellent agreement with available experimental data. Then, the same approach is applied to predict electronic and optical properties of lonsdaleite Ge. We portray lonsdaleite Ge as a direct semiconductor with only weakly dipole-active lowest optical transitions, small band gap, huge crystalfield splitting, and strongly anisotropic effective masses. The unexpectedly small direct gap and the oscillator strengths of the lowest optical transitions are explained in terms of symmetry and back-folding of energy bands of the diamond structure.